# Using and Converting Units

We use equations to express relationships among physical quantities, represented by algebraic symbols. Each algebraic symbol always denotes both a number and a unit. For example, d might represent a distance of 10 m, t a time of 5 s, and v a speed of 2 m>s.

An equation must always be dimensionally consistent. You can’t add apples and automobiles; two terms may be added or equated only if they have the same units. For example, if a body moving with constant speed v travels a distance d in a time t, these quantities are related by the equation

d = vt

If d is measured in meters, then the product vt must also be expressed in meters. Using the above numbers as an example, we may write

10 m = (2 m/s)(5s)

Because the unit s in the denominator of m>s cancels, the product has units of meters, as it must. In calculations, units are treated just like algebraic symbol with respect to multiplication and division.

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